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Author: Sajjad Najafi
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Languages : en
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I study the dynamic pricing problem of a firm selling limited inventory of multiple differentiated products over a finite planning horizon, where the firm wishes to maximize the expected revenue. I formulate the firm's optimization problem as a Markov decision process and investigate the pricing problem in the presence of a variety of operational settings. First, I integrate consumer's sequential search behavior into the pricing problem. The consumer inspects products one at a time by incurring non-zero search cost, and makes decision by comparing the utility of the best product so far versus the reservation utility, a threshold at which the consumer is indifferent between continuation and stopping of the sequential search. The firm aims at maximizing the expected revenue by offering the products in the right sequence and at the right prices. I analytically derive the optimal prices in each period. I show that under some condition it is optimal to present products in the descending order of quality. Second, I address a problem in which the firm is subject to a set of sales volume constraints required to be satisfied at different time points along the sales horizon. Due to stochastic nature of sales, I incorporate a risk measure that allows the firm to manage the total sales while the expected revenue is maximized. I formulate the problem as a chance-constrained dynamic programming and show that the Karush-Kuhn-Tucker conditions are not only necessary but also sufficient for the optimal price. Third, I assimilate consumer's consideration sets to the dynamic pricing problem. When to make a purchase decision, consumers use a two-stage decision-making process, i.e., consumers constitute a consideration set including a subset of the available products using a screening rule (e.g., brands, quality, and budget), and they only evaluate the products in the consideration set using a utility comparison process and opt for the product with the maximum utility. I show that the first-order condition is sufficient for the optimal price of products if consumers apply a quality-based screening rule.
Author: Sajjad Najafi
Publisher:
ISBN:
Category :
Languages : en
Pages :
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Book Description
I study the dynamic pricing problem of a firm selling limited inventory of multiple differentiated products over a finite planning horizon, where the firm wishes to maximize the expected revenue. I formulate the firm's optimization problem as a Markov decision process and investigate the pricing problem in the presence of a variety of operational settings. First, I integrate consumer's sequential search behavior into the pricing problem. The consumer inspects products one at a time by incurring non-zero search cost, and makes decision by comparing the utility of the best product so far versus the reservation utility, a threshold at which the consumer is indifferent between continuation and stopping of the sequential search. The firm aims at maximizing the expected revenue by offering the products in the right sequence and at the right prices. I analytically derive the optimal prices in each period. I show that under some condition it is optimal to present products in the descending order of quality. Second, I address a problem in which the firm is subject to a set of sales volume constraints required to be satisfied at different time points along the sales horizon. Due to stochastic nature of sales, I incorporate a risk measure that allows the firm to manage the total sales while the expected revenue is maximized. I formulate the problem as a chance-constrained dynamic programming and show that the Karush-Kuhn-Tucker conditions are not only necessary but also sufficient for the optimal price. Third, I assimilate consumer's consideration sets to the dynamic pricing problem. When to make a purchase decision, consumers use a two-stage decision-making process, i.e., consumers constitute a consideration set including a subset of the available products using a screening rule (e.g., brands, quality, and budget), and they only evaluate the products in the consideration set using a utility comparison process and opt for the product with the maximum utility. I show that the first-order condition is sufficient for the optimal price of products if consumers apply a quality-based screening rule.
Author: Oben Ceryan
Publisher:
ISBN:
Category :
Languages : en
Pages : 40
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Firms that offer multiple products are often susceptible to periods of inventory mismatches where one product may face shortages while the other has excess inventories. In this paper, we study a joint implementation of price- and capacity-based substitution mechanisms to alleviate the level of such inventory disparities. We consider a firm producing substitutable products via a capacity portfolio consisting of both product dedicated and flexible resources and characterize the structure of the optimal production and pricing decisions. We then explore how changes in various problem parameters affect the optimal policy structure. We show that the availability of a flexible resource helps maintain stable price differences across products over time even though the price of each product may fluctuate over time. This result has favorable ramifications from a marketing standpoint as it suggests that even when a firm applies a dynamic pricing strategy, it may still establish consistent price positioning among multiple products if it can employ a flexible replenishment resource. We provide numerical examples for the price stabilization effect and discuss extensions of our results to a more general multiple product setting.
Author: Ying Cao (Ph. D.)
Publisher:
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Category : Advertising
Languages : en
Pages :
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This dissertation consists of three essays which study assortment planning and inventory management of substitutable products motivated by different practical problems. Chapter 2 considers the assortment planning problem for a retailer who faces customers that buy multiple differentiated products (n-pack) on a store visit. We develop two choice models: the probabilistic choice rule which captures the heterogeneous consumer population choice pattern and maximum choice rule which captures the homogeneous consumer population choice pattern. We find that, under probabilistic choice rule, the optimal assortment is such that it includes a certain number of the most and least popular products. In contrast, under maximum choice rule, the optimal assortment does not have a fixed structure except that it is guaranteed to include the most popular product. We develop an algorithm under maximum choice rule which is shown to have good performance. In addition, we derive the structure of optimal assortment under both choice rules when a retailer ignores key features of n-pack choice model including choice premium and basket shopping behavior. We also conduct a numerical study where we show that ignoring these key features can lead to significant profit loss for a retailer. Chapter 3 explores the assortment planning for a firm who faces a two-sided market. That is, the firm receives revenues from two distinct user groups: the customers, who pay for the products it sells and the advertisers who pay to advertise their brand to the customers. We obtain structural properties of the optimal assortment. We also consider the case where the firm is allowed to offer multiple products with the same attractiveness profile and price. In this case, we obtain conditions under which the optimal assortment is made out of distinct products. In addition, we show that ignoring the revenue from the customers or the advertisers, or focusing only on one segment when making product assortment decisions can lead to a significant revenue loss; specifically, we derive the theoretical bound on revenue loss in these situations. Chapter 4 studies the decision making of an inventory manager who needs to decide order quantities of multiple substitutable products in his store. As such, the decision maker typically checks the sales history of the products. When there is stock-out, the sales history provides inaccurate information because the lost sales are unobservable and the sales from substitution are indistinguishable from first-choice sales, which we refer to as the "doublecensoring effect". To study the impact of substitution rate and information amount on decision maker's performance, we design an experiment where subjects need to decide inventory levels for 2 substitutable products in consecutive 30 periods. The experimental data shows that subjects underestimate the demand for high demand product and overestimate the demand for low demand product. Moreover, the bias is worse when there is substitution in fully censored information treatment. Also, when subjects are provided with less information, they tend to order larger quantity in early periods in order to learn demand.
Author: Ching-jen Sun
Publisher:
ISBN:
Category : Prices
Languages : en
Pages : 120
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Abstract: This dissertation develops three essays on dynamic pricing to investigate two important topics in industrial organization: price dispersion and price discrimination. The first essay considers a stylized model of dynamic price competition in which each seller sells one unit of a homogeneous commodity by posting prices in every period to maximize the expected profits with discounting. A random number of buyers come to the market in each period. Each buyer demands at most one unit of the good, and they all have a common reservation price. They know all prices posted by all firms in the market; hence search is costless. I show that when there is a positive probability of excess demand, the model has a unique (symmetric) mixed-strategy equilibrium. In this equilibrium, each seller posts a price in every period according to a non-degenerate distribution, which is determined by the number of sellers remaining in the market in that period. Sellers play mixed strategies as they are indifferent between selling sooner at a lower price and waiting to sell at a higher price later. Thus, price dispersion not only exists in every period among firms, but also persists over time. In the second essay, I consider a monopolist who can sell vertically differentiated products over two periods to heterogeneous consumers. Consumers each demand one unit of the product in each period. In the second period, consumers are sorted into different segments according to their first-period choice, and the monopolist can offer different menus of contracts to different segments. In this way, the monopolist can price discriminate consumers not only by product quality, but also by purchase history. I fully characterize the monopolist's optimal pricing strategy when the type space is discrete and a simple condition is given to determine whether the monopolist should price discriminate consumers by product quality in the first period. When the consumers' type space is a continuum, I show that there is no fully separating equilibrium, and some properties of the optimal menu of contracts (price-quality pairs) are characterized within the class of partition PBE (Perfect Bayesian Equilibrium). The monopolist will offer only one quality in the first period when the social surplus function is log submodular or the firm and consumers are patient. If it is optimal for the firm to offer only one quality in the first period, the optimal market coverage in the first period is smaller than that in the static model. Furthermore, in equilibrium there are some high-type consumers choosing to downgrade the product in the second period, a phenomenon that has never been addressed in the literature. In the second essay, when the consumers' type space is a continuum, the analysis of the optimal menu of contracts is restricted within the class of partition PBE. The third essay provides a justification for this qualification. I ask whether an optimal menu of contracts can induce a non-partition continuation equilibrium by scrutinizing the example constructed by Laffont and Tirole (1988). They construct a non-partition continuation equilibrium for a given first-period menu of incentive contracts and conjecture that this continuation equilibrium need not be suboptimal for the whole game under small uncertainty. I construct two first-period incentive schemes leading to a partition continuation equilibrium and show that, regardless of the extent of uncertainty, their non-partition continuation equilibrium generates a smaller payoff than one of two partition continuation equilibria for the principal. In this sense, Laffont and Tirole's menu of contracts, giving rise to a non-partition continuation equilibrium, is not optimal. I provide an intuition behind this result, hoping to shed light on the problem of dynamic contracting without commitment.
Author: 蔡文真
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ISBN:
Category :
Languages : en
Pages :
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Author: Koray Cosguner
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Category :
Languages : en
Pages : 0
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Author: Wenjing Shen
Publisher: ProQuest
ISBN: 9780549994619
Category :
Languages : en
Pages : 161
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Author: EunMi Lee
Publisher:
ISBN:
Category :
Languages : en
Pages : 57
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This study develops a dynamic pricing model with a quality substitutable product, taking into account strategic and myopic consumers. In each of the two periods, the firm can choose between offering a high quality product, a low quality product or both and the corresponding price for the product. Strategic consumers compare current utility with future utility in order to decide the time of purchase and the quality of the product in an attempt to maximize their utilities. Myopic consumers consider only current utility in purchasing of the products. We generate scenarios, prove whether a scenario is feasible and which scenario produces the best profit for the firm. Our result suggests that the firm obtains the best profit when it provides only high quality products in each of the two periods. In other words, the firm does not have to offer quality substitution as intertemporal substitution suffices to maximize the expected profit.
Author: Qian Liu
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ISBN:
Category :
Languages : en
Pages : 35
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Opaque selling, in which a seller offers a menu of opaque products from a collection of physical products, has been shown to be an effective strategy to segment a market and improve the seller's profit. We study opaque selling with stochastic demand and fixed initial inventory, where we consider two scenarios. In the exogenous fulfillment scenario, the assignment of physical products to fulfill customer demand is based on pre-announced probabilities. In the endogenous fulfillment scenario, the assignment is dynamically determined by the seller. In both settings, the seller dynamically controls the offering of opaque products over time to maximize the total expected revenue. The existing literature has well studied the mechanism of opaque selling and its benefits over other selling strategies. However, much of the literature considers only a single opaque product. This paper contributes to the literature by considering multiple opaque products and focusing on the practice implementation of opaque selling. We formulate the seller's problem as a stochastic dynamic program. Due to the well-known curse of dimensionality, we study the fluid control problem and develop decomposition heuristic for both scenarios based on the corresponding fluid solution. We show that the fluid control problem can provide a time-based fluid policy that is asymptotically optimal. In particular, we show that adopting a stationary probabilistic fulfillment strategy for the endogenous fulfillment scenario is asymptotically optimal. The numerical study shows that offering multiple opaque products can substantially improve the seller's revenue under certain conditions. Our results provide guidance for sellers on how to implement the opaque selling practically when they have finite inventories of multiple substitutable products.
Author: Rainer Schlosser
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Category :
Languages : de
Pages :
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